This invention relates to a picture deforming process in which digital picture data obtained by scanning and sampling an original picture by the picture element are processed to reproduce a picture with a picture element pitch different from that employed in reading the original picture.
In general, in digital picture input and output devices such as facsimile devices, their output picture element pitches are fixed. Therefore, in order to enlarge, contract or incline an original picture, i.e. to geometrically deform the original picture, it is necessary that the original picture is subjected to deformation process, i.e. the original picture is sampled again with a picture element pitch different from that employed in the previous or initial reading of the original picture, thereby to output picture data subjected to deformation process for every picture element.
Heretofore, for instance in the case where magnification variation is carried out according to a picture deforming process of this type, predetermined processes (as described below) are successively carried out for every picture element thereby to process the entire picture on the basis of the fundamental principle that if a picture element at a position a on a picture is sampled againat a position b, then the magnification of the picture can be varied, as shown in FIG. 1. That is, a method is employed in which, under the conditions that in FIG. 1 the coordinates of a picture element on an original picture is (i,j) with pitches px and py and the coordinates of a picture element on the magnification-varied picture is (k,l) with pitches qx and qy, a magnification-varied picture element S(k,l) is represented by using four picture elements F(i,j), F(i+1, j), F(i, j+1) and F(i+1, j+1) of the original picture surrounding the picture element S(k,l). In this connection, it is assumed that the original point of the coordinate (i,j) system of the picture elements of the original picture is at the same position as that of the original point of the coordinate (k,l) system of the picture elements of the magnification-varied picture. However, even if these original points are at different positions, no problem is caused in the production of the magnification-varied picture.
In the method, parameter conversion is carried out according to the following expressions in order to represent the coordinate (i,j) system and the coordinate (k,l) system with a common rectangular coordinate system (x,y): EQU Rx.ident.px/qx, Ry.ident.py/qy (1)
where Rx is the magnification variation factor in the direction of x, and Ry is the magnification variation factor in the direction of y. ##EQU1## EQU i=[xi], j=[yj] (3)
where [xi] and [yj] are the maximum integers not larger than x and y in the common coordinate system (x,y), respectively.
Therefore, the position (.DELTA.x,.DELTA.y) on the x-y coordinate system of the magnification-varied picture element S(k,l) with the original picture element F(i,j) as the original point can be obtained from the following equations (4) as is apparent from the relationships indicated in FIG. 1: ##EQU2## Thus, the density level of the magnification-varied picture element S(k,l) can be interpolated by a plurality of original picture elements F(i+i', j+j') (where --M&lt;i'&lt;M+1, and -N&lt;j'&lt;N+1) surrounding it.
A variety of interpolation methods are known in the art. One of the interpolation methods is a minimum error interpolation method employing a sine function. By way of example, a picture deforming process utilizing the minimum error interpolation method will be described. However, it should be noted that picture deforming processes employing other interpolation methods can similarly process pictures merely by using different functions.
In the interpolation method using the sine function, the weight coefficient g(ri) of an estimated picture element S(k,l) is determined by the distances between the picture elements S(k,l) and the original picture elements surrounding it. If the distance (ri) are long, then the weight coefficient becomes excessively small. Therefore, the range of the value (ri) is usually 0.ltoreq.ri.ltoreq.2. The weight coefficient g(ri) is a sine function as expressed by the following equation (5): ##EQU3##
The density level of a magnification-varied picture element S(k,l) is determined by using the various parameters obtained as described above, according to the steps indicated in FIG. 2. First, the magnification variation factors Rx and Ry are set, and the address of an output picture element to be subjected to magnification variation is set. Thereafter, in the step B, calculations are carried out according to the equations (2) and (3) described above. In the step C, the data of 2M.times.2N original picture elements surrounding a picture element F(i,j) are read out. Between the steps D and E, calculation is carried out according to the equation (4), and according to the results of calculation a weight coefficient g{r(i',j')} corresponding to the distances r(i',j') between the output picture element S(k,l) and the surrounding picture elements is calculated. Finally, in the step E, a process for deterimining the density level of the output picture element S(k,l) is carried out.
As is clear from the above description, in the conventional picture deforming process, a number of processes must be carried out for every output picture element as shown in FIG. 2. Accordingly, the processing time is considerably long; and not only adders and subtractors but also integrators and function generators are required for carrying out the various processes, with the result that the device is intricate in arrangement and high in manufacturing cost.